Instructions:
1. Melt 2 tablespoons butter in a large heavy, oven-safe skillet. Sauté onion and garlic in butter, until translucent, about 2-3 minutes.
2. Add 2 tablespoons butter and shredded sprouts, and sauté for 5 minutes. Season with salt and pepper.
3. In a bowl, combine mashed potatoes and sautéed Brussels sprouts. Melt 2 tablespoons butter in skillet and add the mixture, pressing down slightly over top. Let brown, undisturbed, 8-10 minutes.
4. Once the bottom is browned, carefully turn patty by loosening around edges with a spatula. Set a large plate over skillet. Holding the plate on the top, flip, turning onto plate. Add 2 more tablespoons butter to the pan and stir until melted. Then slide the cake into the pan, browned side up.
5. When the second side is browned, top with grated cheese, run under the broiler just until the cheese is melted.
6. Serve in wedges straight from the pan.